Inverse Function Theoremlocal existence resultWe introduce different notions of invertibility for generalized functions in the sense of Colombeau. Several necessary conditions for (left, right) invertibility are derived, giving rise to the concepts of compactly asymptotic injectivity and surjectivity. We ...
The following result proves the necessary and sufficient condition for the existence of a semi-E-convex function at a point. Theorem 2.5. Suppose f : M → R and E : Rn → Rn are differentiable functions. Let E be a homeomorphism and let x be a fixed point of E. Then, f is semi-...
The chapter describes the notion of subspaces and adjoint subspaces and proves, under hypotheses almost immediately applicable to differential subspaces, a representation theorem. The chapter presents definition of the generalized inverse of a subspace and lists some of its properties. As an example of...
Theorem 2.11 Let Ω0 be a domain in Rp+1 and f0:Ω0→Rp+q be a real analytic function. Then the function given by CK[f0](xx)=exp(xx_qDxxp)f0(xxp)=∑k=0+∞1k!(xx_qDxxp)kf0(xxp),xx=xxp+xx_q, is a generalized partial-slice monogenic function f∗ defined in Ω⊆Ω0...
Clarke FH (1976) On the inverse function theorem. Pacif J Math 64:97–102 Google Scholar Fitzpatrick S, Phelps R (to appear) Differentiability of the metric projection in Hilbert spaces. Hestenes M (1975) Optimization theory: The finite dimensional case. Wiley, New York Google Scholar Hiria...
We establish the existence and some properties for the GIT, the GCP and the inverse integral transform. Finally, we prove a Fubini theorem for the GIT and the GCP.View full textDownload full textCorrectionKeywordsgeneralized integral transform, generalized convolution product, inverse integral ...
However, if we can guess a trial solution m0 that is close to the minimum error solution, then we can use Taylor's theorem to approximate E(m) as a low order polynomial centered about this point. If m0 is close enough to the minimum that a quadratic approximation will suffice, then ...
the generalized composite commodity theorem and food demand:广义复合商品定理与食品需求 热度: A Generalized Courant-Fischer Minimax Theorem(广义Courant-Fischer极小极大定理) 热度: Unified fractional fourier transform and sampling theorem - :统一的分数傅里叶变换和采样定理- 热度: 相关推荐 IEEE ...
{\beta }_*)\)is nonsingular when n is large enough. Therefore, it follows from the inverse function theorem that within a small neighborhood of\(\varvec{\beta }_*\), there exists a unique solution\(\hat{\varvec{\beta }}\)to\(U(\varvec{\beta })=0\)for sufficiently large n. ...
Theorem 3 The initial value problem(w′)3 The case (p,q)=(3/2,2) We now turn to a consideration of the initial value problem(w′)3=(1−w2)2,w(0)=0. In [10] Takeuchi leaves open the task of finding a duplication formula for the solution sin3/2,2 to this problem. In [...